What is the moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about its diameter?
Show Hint
- \( \frac{2}{5} M R^2 \)
- \( \frac{1}{2} M R^2 \)
- \( \frac{3}{5} M R^2 \)
- \( M R^2 \)
The Correct Option is A
Solution and Explanation
Given: Mass of the sphere, \( M \)
Radius of the sphere, \( R \)
Step 1: Moment of Inertia Formula for a Solid Sphere The moment of inertia of a solid sphere about an axis through its diameter is \( I = \frac{2}{5} M R^2 \), where \( M \) is the sphere's mass and \( R \) is its radius.
Step 2: Result The moment of inertia of the solid sphere about its diameter is \( \frac{2}{5} M R^2 \).
Answer: The correct answer is option (a): \( \frac{2}{5} M R^2 \).
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